Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient

P. A. Farrell; A. F. Hegarty; J. J.H. Miller; E. O'Riordan; G. I. Shishkin

doi:10.1016/j.mcm.2005.01.025

Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient

P. A. Farrell
, A. F. Hegarty
, J. J.H. Miller
, E. O'Riordan
, G. I. Shishkin

Research output: Contribution to journal › Article › peer-review

Abstract

A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter ε, is examined. Due to the discontinuity an interior layer appears in the solution. A finite difference method is constructed for solving this problem, which generates ε-uniformly convergent numerical approximations to the solution. The method uses a piecewise uniform mesh, which is fitted to the interior layer, and the standard upwind finite difference operator on this mesh. The main theoretical result is the ε-uniform convergence in the global maximum norm of the approximations generated by this finite difference method. Numerical results are presented, which are in agreement with the theoretical results.

Original language	English
Pages (from-to)	1375-1392
Number of pages	18
Journal	Mathematical and Computer Modelling
Volume	40
Issue number	11-12
DOIs	https://doi.org/10.1016/j.mcm.2005.01.025
Publication status	Published - Dec 2004

Keywords

Difference scheme
Discontinuous coefficient
Interior layer
Piecewise-uniform mesh
Singularly perturbed ODE

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10.1016/j.mcm.2005.01.025

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title = "Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient",

abstract = "A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter ε, is examined. Due to the discontinuity an interior layer appears in the solution. A finite difference method is constructed for solving this problem, which generates ε-uniformly convergent numerical approximations to the solution. The method uses a piecewise uniform mesh, which is fitted to the interior layer, and the standard upwind finite difference operator on this mesh. The main theoretical result is the ε-uniform convergence in the global maximum norm of the approximations generated by this finite difference method. Numerical results are presented, which are in agreement with the theoretical results.",

keywords = "Difference scheme, Discontinuous coefficient, Interior layer, Piecewise-uniform mesh, Singularly perturbed ODE",

author = "Farrell, \{P. A.\} and Hegarty, \{A. F.\} and Miller, \{J. J.H.\} and E. O'Riordan and Shishkin, \{G. I.\}",

year = "2004",

month = dec,

doi = "10.1016/j.mcm.2005.01.025",

language = "English",

volume = "40",

pages = "1375--1392",

journal = "Mathematical and Computer Modelling",

issn = "0895-7177",

number = "11-12",

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TY - JOUR

T1 - Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient

AU - Farrell, P. A.

AU - Hegarty, A. F.

AU - Miller, J. J.H.

AU - O'Riordan, E.

AU - Shishkin, G. I.

PY - 2004/12

Y1 - 2004/12

N2 - A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter ε, is examined. Due to the discontinuity an interior layer appears in the solution. A finite difference method is constructed for solving this problem, which generates ε-uniformly convergent numerical approximations to the solution. The method uses a piecewise uniform mesh, which is fitted to the interior layer, and the standard upwind finite difference operator on this mesh. The main theoretical result is the ε-uniform convergence in the global maximum norm of the approximations generated by this finite difference method. Numerical results are presented, which are in agreement with the theoretical results.

AB - A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter ε, is examined. Due to the discontinuity an interior layer appears in the solution. A finite difference method is constructed for solving this problem, which generates ε-uniformly convergent numerical approximations to the solution. The method uses a piecewise uniform mesh, which is fitted to the interior layer, and the standard upwind finite difference operator on this mesh. The main theoretical result is the ε-uniform convergence in the global maximum norm of the approximations generated by this finite difference method. Numerical results are presented, which are in agreement with the theoretical results.

KW - Difference scheme

KW - Discontinuous coefficient

KW - Interior layer

KW - Piecewise-uniform mesh

KW - Singularly perturbed ODE

UR - https://www.scopus.com/pages/publications/18044373276

U2 - 10.1016/j.mcm.2005.01.025

DO - 10.1016/j.mcm.2005.01.025

M3 - Article

AN - SCOPUS:18044373276

SN - 0895-7177

VL - 40

SP - 1375

EP - 1392

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

IS - 11-12

ER -

Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient

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Keywords

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